CBSE Class 10 Mathematics Triangles Assignment Set 02

IMPORTANT CONCEPTS

TAKE A LOOK

1. Similar Triangles:- Two triangles are said to be similar, if (a) Their corresponding angles are equal and (b) Their corresponding sides are in proportion (or are in the same ratio).

2. Basic proportionality Theorem [ or Thales theorem for solution refer NCERT Text Book ].

3. Converse of Basic proportionality Theorem.

4. Criteria for similarity of Triangles.

(a) AA or AAA similarity criterion.

(b) S.A.S similarity criterion.

(c) S.S.S similarity criterion.

5. Areas of similar triangles.

6. Pythagoras theorem.

7. Converse of Pythagoras theorem.

Question. If in two triangles DEF and PQR, –D = –Q and –R = –E, then which of the following is not true?
(a) PR/EF = PQ/DF 
(b) PQ/DE = RP/EF
(c) QR/DE = PQ/DF
(d) RP/EF = QR/DE

Answer : B

Question. In ΔABC and ΔDEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are
(a) congruent but not similar
(b) similar but not congruent
(c) neither congruent nor similar
(d) congruent as well as similar

Answer : B

Question. In the figure shown along side, DE || BC, ∠ADE = 70° and ∠BAC = 50°, then ∠BCA =

(a) 30°
(b) 60°
(c) 40°
(d) 45°

Answer : B

Question. In the figure, if ∠ACB = ∠CDA, AC = 6 cm and AD = 3 cm, then the length of AB is

(a) 8 cm
(b) 10 cm
(c) 12 cm
(d) 16 cm

Answer : C

Question. In the given figure, if DE || BC, the EC equals

(a) 1 cm
(b) 2 cm
(c) 4 cm
(d) 6 cm

Answer : B

Question. In the given figure, D and E are points on AB and AC respectively such that DE || BC. If AD = 1/3 BD and AE = 4.5 cm, then AC is equal to

(a) 12 cm
(b) 14 cm
(c) 16 cm
(d) 18 cm

Answer : D

Question. If ABC and EBC are two equilateral triangles such that D is mid-point of BC, then the ratio of the areas of triangles ABC and BDE is
(a) 2 : 1
(b) 1 : 2
(c) 1 : 4
(d) 4 : 1

Answer : D

Question. Given ΔABC ~ ΔDEF, if AB = 2DE and area of ΔABC is 56 cm2, find the area of ΔDEF.
(a) 14 sq.cm
(b) 5 sq.cm
(c) 18 sq.cm
(d) 56 sq.cm

Answer : A

Question. The area of a right angled triangle is 40 sq. cm. and its perimeter is 40 cm. The length of its hypotenuse is
(a) 16 cm
(b) 18 cm
(c) 17 cm
(d) Data insufficient

Answer : B

Question. Two triangles are similar if
(a) their corresponding angles are equal.
(b) their corresponding sides are equal.
(c) both are right triangle.
(d) None of the above

Answer : A

Question. Which of the following is/are not correct?
(a) If the diagonals of a quadrilateral divide each other proportionally, then it is a trapezium.
(b) The line segments joining the mid-points of the adjacent sides of a quadrilateral form a parallelogram.
(c) If corresponding sides of two similar triangles are in the ratio 4 : 5, then corresponding medians of the triangles must be in the ratio 4 : 5.
(d) None of the above

Answer : D

Fill in the Blanks

DIRECTIONS : Complete the following statements with an appropriate word / term to be filled in the blank space(s).

Question. All circles are ..................
Answer : similar

Question. All squares are ..................
Answer : similar

Question. All ........... triangles are similar.
Answer : equilateral

Question. Two polygons of the same number of sides are similar, if their corresponding angles are ......... and their corresponding sides are in the same ...........
Answer : equal , ratio

Question. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the ............. ratio.
Answer : same

Question. If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the .............. side.
Answer : third

Question. All congruent figures are similar but the similar figures need ............. be congruent.
Answer : not

Question. Two polygons of the same number of sides are similar, if all the corresponding angles are .............
Answer : equal

Question. The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO = CO/DO. ABCD is a .............
Answer : trapezium

Question. A line drawn through the mid-point of one side of a triangle parallel to another side bisects the ............. side.
Answer : third

Question. Line joining the mid-points of any two sides of a triangle is ............. to the third side.
Answer : parallel

Question. In DABC, AB = 6√3 m, AC = 12 cm and BC = 6 cm, then ∠B = .................. .
                                       OR
Two triangles are similar if their corresponding sides are .................. .
Answer : [90°]
∴ AB² + BC² = 108 + 36 = 144 = AC²
So, AC is hypotenuse and ∠B = 90°.
             OR
[Proportional]

True / False

DIRECTIONS : Read the following statements and write your answer as true or false.

Question. Two figures having the same shape but not necessarily the same size are called similar figures.
Answer : True

Question. All the congruent figures are similar but the converse is not true.
Answer : True

Question. If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.
Answer : True

Question. If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar.
Answer : True

Question. If in two triangles, corresponding sides are in the same ratio, then their corresponding angles are equal and hence the triangles are similar.
Answer : True

Question. If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio (proportional), then the triangles are similar.
Answer : True

Question. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Answer : True

Question. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Answer : True

Question. If, in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.
Answer : True

Question. Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O, OA/OC = OB/OD
Answer : True

Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Choose the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): If ΔABC and ΔPQR are congruent triangles, then they are also similar triangles.
Reason (R): All congruent triangles are similar but the similar triangles need not be congruent.
Answer : A

Question. Assertion (A): In the given figure, PA || QB || RC || SD.
Reason (R): If three or more line segments are perpendiculars to one line, then they are parallel to each other.
Answer : A